(1) referring to the Champs-Élysées in Paris
(2) "pop at the surface" - as petite élève says in the comments, he's referring to wanting to die a bigwig
(3) this is a pun on words in French, "grosses coupures" can mean both "big cuts/wounds" (referring to self-mutilation) and also "big money". Kind of impossible to keep that in English

ta mère la pute -> what would be a rap song without a bit of gratuitous profanity, eh? That would roughly translate as "you motherfucker" or "you son of a bitch". It's probably somewhere in between in terms of intensity and vulgarity.